CRLB-Driven Beamforming and Power Allocation for Multi-BS Cooperative ISAC Networks

This paper presents a Cramér-Rao lower bound (CRLB)-driven beamforming (BF) and power allocation (PA) framework for cooperative integrated sensing and communication (ISAC) networks, where a set of multi-antenna base stations (BSs) jointly serve multiple users and simultaneously perform multi-static target estimation. In our design, we investigate how the position error bound (PEB) and velocity error bound (VEB) can be exploited and incorporated into BF and PA optimization. The design leveraging PEB and VEB as metrics directly characterizes sensing accuracy. First, we propose a semidefinite programming (SDP)-based BF, where the PEB and VEB constraints are handled by double Schur complements, and the rank-1 constraints of the BF covariance matrices are relaxed by semidefinite relaxation (SDR), whose tightness is proved using the Karush-Kuhn-Tucker (KKT) conditions. Addressing the complexity, we further develop a two-stage PA algorithm, where the communication and sensing beams are formed by the regularized zero-forcing (RZF) and null-space projection (NSP) methods, respectively, and the communication and sensing PAs are solved sequentially by second-order cone programming (SOCP). Although the PA algorithm sacrifices the degrees of freedom, its performance shows a slight gap compared to BF in the simulation, while the execution time of around 25 ms demonstrates its applicability in dynamic environments.

ERNIE 5.0 Technical Report

In this report, we introduce ERNIE 5.0, a natively autoregressive foundation model desinged for unified multimodal understanding and generation across text, image, video, and audio. All modalities are trained from scratch under a unified next-group-of-tokens prediction objective, based on an ultra-sparse mixture-of-experts (MoE) architecture with modality-agnostic expert routing. To address practical challenges in large-scale deployment under diverse resource constraints, ERNIE 5.0 adopts a novel elastic training paradigm. Within a single pre-training run, the model learns a family of sub-models with varying depths, expert capacities, and routing sparsity, enabling flexible trade-offs among performance, model size, and inference latency in memory- or time-constrained scenarios. Moreover, we systematically address the challenges of scaling reinforcement learning to unified foundation models, thereby guaranteeing efficient and stable post-training under ultra-sparse MoE architectures and diverse multimodal settings. Extensive experiments demonstrate that ERNIE 5.0 achieves strong and balanced performance across multiple modalities. To the best of our knowledge, among publicly disclosed models, ERNIE 5.0 represents the first production-scale realization of a trillion-parameter unified autoregressive model that supports both multimodal understanding and generation. To facilitate further research, we present detailed visualizations of modality-agnostic expert routing in the unified model, alongside comprehensive empirical analysis of elastic training, aiming to offer profound insights to the community.